Related papers: A note on delay-inverse systems, I
A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…
We discuss a recent line of research investigating inverse theorems with respect to general k-wise correlations, and explain how such correlations arise in different contexts in mathematics. We outline some of the results that were…
Loday's dendriform algebras and its siblings pre-Lie and zinbiel have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each individual…
We survey Lawvere theories at the level of infinity categories, as an alternative framework for higher algebra (rather than infinity operads). From a pedagogical perspective, they make many key definitions and constructions less technical.…
Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction for characteristic matrices for systems of linear delay-differential equations with periodic coefficients. First, we show that matrices constructed in this way…
Drazin inverses are a special kind of generalized inverses that can be defined for endomorphisms in any category. A natural question to ask is whether one can somehow extend the notion of Drazin inverse to arbitrary maps - not simply…
In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new…
A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…
We introduce the concept of inverse powerset by adding three axioms to the Zermelo-Fraenkel set theory. This extends the Zermelo-Fraenkel set theory with a new type of set which is motivated by an intuitive meaning and interesting…
The Ehrhart polynomial and Ehrhart series count lattice points in integer dilations of a lattice polytope. We introduce and study a $q$-deformation of the Ehrhart series, based on the notions of harmonic spaces and Macaulay's inverse…
We study the cardinal invariants of measure and category after adding one random real. In particular, we show that the number of measure zero subsets of the plane which are necessary to cover graphs of all continuous functions maybe large…
Curved A-infinity algebras appear in nature as deformations of dg algebras. We develop the basic theory of curved A-infinity algebras and, in particular, curved dg algebras. We investigate their link with a suitable class of dg coalgebras…
We introduce a new class of collider-type observables in conformal field theories which we call generalized event shapes. They are defined as matrix elements of light-ray operators that are sensitive to the longitudinal, or time-dependent,…
The purpose of this paper is to define some notions of movability for morphisms of inverse systems which extend the movability properties of inverse systems and which are compatible with the equivalence relations which define pro-morphisms…
The article continues the study of the 'regular' arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification…
A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…
We investigate an enriched-categorical approach to a field of discrete mathematics. The main result is a duality theorem between a class of enriched categories (called $\overline{\mathbb{Z}}$- or $\overline{\mathbb{R}}$-categories) and that…
Generalizing a result of Masuti and the second author, we describe inverse limits of Macaulay's inverse systems for Cohen-Macaulay factor algebras of formal power series or polynomial rings over an infinite field. On the way we find a…
The paper is devoted to construction of some closed inductive sequence of models of the generalized second-order Dedekind theory of real numbers with exponentially increasing powers. These models are not isomorphic whereas all models of the…
We use the theory of $x-y$ duality to propose a new definition / construction for the correlation differentials of topological recursion; we call it "generalized topological recursion". This new definition coincides with the original…